1. Field of the Invention
The present invention relates to a method of monitoring a change in thickness of a conductive film formed on a surface of a substrate during polishing and also relates to a polishing apparatus and a monitoring apparatus.
2. Description of the Related Art
A polishing apparatus is widely used for polishing a conductive film, such as a barrier film and an interconnect metal film, formed on a surface of a wafer. Polishing end point detection and a change in polishing conditions during polishing are determined based on a thickness of the conductive film. Thus, the polishing apparatus usually includes a film-thickness detector for detecting a thickness of the conductive film during polishing. A typical example of this film-thickness detector is an eddy current sensor. This eddy current sensor is configured to supply a high-frequency alternating current to a coil so as to induce an eddy current in the conductive film to thereby detect the thickness of the conductive film from a change in impedance caused by a magnetic field of the eddy current induced.
FIG. 1 is a view showing an equivalent circuit for explaining a principle of the eddy current sensor. When an AC power supply 3 sends a high-frequency alternating current I1 to a coil 1, magnetic lines of force, induced in the coil 1, pass through the conductive film. As a result, mutual inductance occurs between a sensor-side circuit and a conductive-film-side circuit, and an eddy current I2 flows through the conductive film. This eddy current I2 creates magnetic lines of force, which cause a change in an impedance of the sensor-side circuit. The eddy current sensor measures the thickness of the conductive film from the change in the impedance of the sensor-side circuit.
In the sensor-side circuit and the conductive film-side circuit in FIG. 1, the following equations hold.R1I1+L1dI1/dt+MdI2/dt=E  (1)R2I2+L2dI2/dt+MdI1/dt=0  (2)where M represents mutual inductance, R1 represents equivalent resistance of the sensor-side circuit including the coil 1, L1 represents self inductance of the sensor-side circuit including the coil 1, R2 represents equivalent resistance of the conductive film in which the eddy current is induced, and L2 represents self inductance of the conductive film through which the eddy current flows.
Letting In=Aneeωt (sine wave), the above equations (1) and (2) are expressed as follows.(R1+jωL1)I1+jωMI2=E  (3)(R2+jωL2)I2+jωMI1=O  (4)
From these equations (3) and (4), the following equations are derived.
                                                                        I                1                            =                            ⁢                                                E                  ⁡                                      (                                                                  R                        2                                            +                                              jω                        ⁢                                                                                                  ⁢                                                  L                          2                                                                                      )                                                  /                                  [                                                                                    (                                                                              R                            1                                                    +                                                      jω                            ⁢                                                                                                                  ⁢                                                          L                              1                                                                                                      )                                            ⁢                                              (                                                                              R                            2                                                    +                                                      jω                            ⁢                                                                                                                  ⁢                                                          L                              2                                                                                                      )                                                              +                                                                  ω                        2                                            ⁢                                              M                        2                                                                              ]                                                                                                        =                            ⁢                              E                /                                  [                                                            (                                                                        R                          1                                                +                                                  jω                          ⁢                                                                                                          ⁢                                                      L                            1                                                                                              )                                        +                                                                  ω                        2                                            ⁢                                                                        M                          2                                                /                                                  (                                                                                    R                              2                                                        +                                                          jω                              ⁢                                                                                                                          ⁢                                                              L                                2                                                                                                              )                                                                                                      ]                                                                                        (        5        )            
Thus, the impedance Φ of the sensor-side circuit is given by the following equation.
                    Φ        =                              E            /                          I              1                                =                                    [                                                R                  1                                +                                                      ω                    2                                    ⁢                                      M                    2                                    ⁢                                                            R                      2                                        /                                          (                                                                        R                          2                          2                                                +                                                                              ω                            2                                                    ⁢                                                      L                            2                            2                                                                                              )                                                                                  ]                        +                          jω              [                                                L                  1                                -                                                      ω                    2                                    ⁢                                      L                    2                                    ⁢                                                            M                      2                                        /                                          (                                                                        R                          2                          2                                                +                                                                              ω                            2                                                    ⁢                                                      L                            2                            2                                                                                              )                                                                                  ]                                                          (        6        )            
Substituting X and Y respectively for a real part (i.e., a resistance component) and an imaginary part (i.e., an inductive reactance component) of the impedance Φ, the following equation is given.(X−R1)2+[Y−ωL1(1−k2/2)]2=(ωL1k2/2)2  (7)
A symbol k in the equation (7) represents coupling coefficient, and the following relationship holds.M=k(L1L2)1/2  (8)
FIG. 2 is a view showing a graph drawn by plotting X and Y, which change with a polishing time, on a XY coordinate system. The coordinate system shown in FIG. 2 is defined by a vertical axis as a Y-axis and a horizontal axis X-axis. Coordinates of a point T∞ are values of X and Y when a thickness of a film is zero, i.e., R2 is zero. Where electrical conductivity of a substrate can be neglected, coordinates of a point T0 are values of X and Y when the thickness of the film is infinity, i.e., R2 is infinity. A point Tn, specified by the values of X and Y, travels in an arc toward the point T0 as the thickness of the film decreases.
FIG. 3 shows a graph obtained by rotating the graph in FIG. 2 through 90 degrees in a counterclockwise direction and further translating the resulting graph. Specifically, the point specified by the coordinates (X, Y) is rotated about the origin O in the XY coordinate system, and the rotated coordinates are further moved so as to create a graph in which a distance between the origin O and the point specified by the coordinates (X, Y) decreases in accordance with a decrease in thickness of the film. A further process, such as amplification, may be applied to the graph in FIG. 3. Although FIG. 3 shows the case where the graph in FIG. 2 is rotated through 90 degrees in the counterclockwise direction, the rotation angle is not limited to 90 degrees. For example, the rotation angle can be adjusted such that the Y-coordinate corresponding to an upper limit of the film thickness to be monitored is equal to the Y-coordinate of the point where the film thickness is zero.
As shown in FIG. 3, the point Tn, positioned from the values of X and Y, travels in an arc toward the point T0, as the thickness of the film decreases. During traveling, an impedance Z(=(X2+Y2)1/2) decreases as the thickness of the film decreases, as long as) the point Tn is not positioned near the point T∞. Therefore, by monitoring the impedance Z, a change in thickness of the film during polishing and a polishing end point can be determined. FIG. 4 shows a graph created by plotting the impedance Z on the vertical axis and a polishing time on the horizontal axis. As shown in this graph, the impedance Z decreases with the polishing time, and becomes constant at a certain time point. Thus, by detecting such a singular point of the impedance Z, the polishing end point can be determined.
Recently, a so-called low-resistance substrate having a very low resistivity (specific resistance) of a substrate itself has been introduced. This low-resistance substrate has a resistivity which is about one thousandth of that of a normal substrate. The substrate having a low resistance provides advantages including realization of low-voltage drive (i.e., larger current can flow using the same voltage) and low on-resistance (i.e., wider applications that require a large current can be achieved).
However, the low-resistance substrate has a sheet resistance that is close to a sheet resistance of a conductive film as an object of polishing. This results in a great influence on the output signal of the eddy current sensor. This problem will be described with reference to FIG. 5. FIG. 5 is a graph showing a locus of the output signal of the eddy current sensor when polishing a tungsten film having a thickness of 100 nm on a substrate (normal substrate) having a normal resistivity, and also showing a locus of the output signal of the eddy current sensor when polishing a tungsten film having the same thickness on a low-resistance substrate. The sheet resistance of the normal substrate is much larger than a sheet resistance of the tungsten film. In this case, it is possible to substantially ignore an effect of the substrate on the output signal of the eddy current sensor. Therefore, the output signal of the eddy current sensor is hardly affected by the sheet resistance of the substrate, and the output signal as in FIG. 5 can be obtained, as long as the film thickness is the same.
On the other hand, the sheet resistance of the low-resistance substrate does not greatly differ from the sheet resistance of the tungsten film. In this case, the output signal of the eddy current sensor is likely to be affected by the low-resistance substrate. As a result, as shown in FIG. 5, the locus of the output signal of the eddy current sensor moves greatly to a large-thickness side as compared with the case of using the normal substrate. In addition, due to a slight difference in resistivity between low-resistance substrates, the locus of the output signal of the eddy current sensor could change as shown in FIG. 5, even when the tungsten film of the same thickness is polished.
Even in this case where the locus of the output signal of the eddy current sensor moves, it is possible to detect the polishing end point since the singular point is drifted as well, as shown in FIG. 6. However, this movement of the output signal leads to problems when stopping polishing or when changing the polishing conditions at a time point when a preset target thickness is reached. This is because of a change in relationship between the values of the output signal of the eddy current sensor and the film thickness. This causes an error in detection of the polishing time.
In addition, there is a difference in degree of a change in the impedance Z indicating the change in film thickness between the normal substrate and the low-resistance substrate. Specifically, as shown in FIGS. 7 and 8, in the normal substrate, an impedance Z1 greatly changes as the film thickness changes. On the other hand, in the low-resistance substrate, an impedance Z2 does not greatly change as the film thickness changes. Such a small change in the impedance Z causes deterioration of a signal-to-noise ratio. As a result, accuracy in detecting the polishing end point and the changing point of the polishing conditions would be lowered.
Moreover, the eddy current sensor has a characteristic such that the output signal thereof changes in accordance with the distance from the conductive film as a target. Consequently, as the distance between the eddy current sensor and the substrate changes due to wear of a polishing pad or the like, the output signal of the eddy current sensor changes as well, in spite of the same film thickness.